A371230
E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 128, 750, 29964, 377160, 15795072, 329631120, 15001287120, 449174341440, 22551082739712, 885381886509120, 49302509206648320, 2391802812599316480, 147728974730632012800, 8502972330919072688640, 580806950108814502345728
Offset: 0
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terms=19; A[]=1; Do[A[x]= 1 - x*A[x]^3*Log[1 - x*A[x]^2] + O[x]^terms//Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]*Range[0,terms-1]! (* Stefano Spezia, Sep 03 2025 *)
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a(n) = n!*sum(k=0, n\2, (2*n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(2*n+1)!;
A371227
E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 56, 390, 6384, 92400, 1812768, 38565072, 949927680, 25934040000, 783458550720, 25909868761920, 930720395219328, 36108805836317760, 1504050682102456320, 66964478742976711680, 3173178938051223889920, 159461567895099436047360
Offset: 0
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a(n) = n!*sum(k=0, n\2, (2*n-2*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-3*k+1)!));
A371228
E.g.f. satisfies A(x) = 1 - x*A(x)*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 80, 510, 12084, 164640, 4272736, 91935648, 2769703920, 80692896240, 2849745645504, 103479044628960, 4250475820200960, 183436357950387360, 8649275730513361920, 430735131434242736640, 22999938416454315239424, 1295673669960473064844800
Offset: 0
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a(n) = n!*sum(k=0, n\2, (2*n-k)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-2*k+1)!));
A371270
E.g.f. satisfies A(x) = 1 + x*A(x)^2 * (exp(x*A(x)^2) - 1).
Original entry on oeis.org
1, 0, 2, 3, 100, 605, 18366, 238147, 7688584, 162016857, 5839673410, 172051422191, 7034104918380, 265080848463301, 12311587474831750, 561485310426413115, 29475848282815342096, 1569372890780660724401, 92402629467727290784650
Offset: 0
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a(n) = n!*(2*n)!*sum(k=0, n\2, stirling(n-k, k, 2)/((n-k)!*(2*n-k+1)!));
A371231
E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^3).
Original entry on oeis.org
1, 0, 2, 3, 152, 930, 42804, 574140, 27267456, 613793376, 31378237200, 1021391030880, 57256014687552, 2456525677525920, 152135168050833408, 8093376365276966400, 554533365688970342400, 35081649646969248529920, 2653840371674014197608448
Offset: 0
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a(n) = n!*(3*n)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(3*n-k+1)!));
A377390
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^2 ).
Original entry on oeis.org
1, 0, 4, 6, 232, 1380, 46308, 593880, 20639456, 434113344, 16557009840, 490894572960, 20995513516800, 801146038080960, 38632110899469696, 1791609186067646400, 97167945389675212800, 5275541489312858803200, 319879838094553691744256, 19820894989178283188198400
Offset: 0
-
a(n) = 2*n!*(2*n+1)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(2*n-k+2)!));
Showing 1-6 of 6 results.